More: In-Depth Discussion of the Reasoning Activities in "Teaching Fractions and Ratios for Understanding"

Time changed; distance from your starting point changed. Your
speed remained constant for the three hours.

2.

Time changed; the surface area of the balloon changed; the volume of
the balloon changed; your puffing rate remained the same for one
minute.

3.

Time changed; your distance from home changed; your speed
remained constant until you got to school.

4.

Time changed; distance from the top of the hill changed; speed
changed.

5.

The cost increases for each subscription option because each
involves a different period of time and a different number of
magazines. However, if you analyze each option in terms of a 3-month
rate, you can see that in each case, the 3-month subscription cost does
not change. Six months costs 2($13.50); 9 months costs 3($13.50), and 12
months costs 4($13.50). Therefore, the same rate applies whether you
buy the magazine for a shorter period of time or for a longer period of
time.

6.

a. The amount of water in the bathtub depends on how long the
water has been running.

a.

How fresh your bread is depends on how many days have passed
Because you baked it.

b.

The amount of postage depends on the weight of your letter.

c.

Your height depends on your age.

7.

a. ↓ ↓ Three books should cost $17.40.

a.

Correct. The time to walk to the mall does not depend on how many
people are walking together.

b.

You cannot correct this statement. People's weights do not work that
way!

c.

↑ ↓ If fewer people work on the project, it will take more time to
complete the project. It will take 5 people 8 weeks to do it.

d.

↑ ↑ It will take less time to write fewer invitations. It will take 24
minutes to write 6 invitations.

e.

The time it takes to drive does not depend on how many people are in
the car. It will still take one person 15 minutes to drive to the game.

f.

The time it takes to swim a lap does not depend on how many people
are swimming together.

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